Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
802 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23766231 | C2 | semidirect |
| 3. #23764237 | C2 | semidirect |
| 4. #23763343 | C2 | semidirect |
| 5. #23761307 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 7. C79×#1507 | C2 | semidirect |
| 9. C2×#14579187 | C4 | semidirect |
| 15. #19098562 | C4 | semidirect |
| 42. C2×#11929608 | C2×C4 | semidirect |
| 60. C22×D4×C79 | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 188. D316 | #99 | semidirect |
| 243. #1507 | D79 | semidirect |
| 246. C79 | #9365 | semidirect |
| 277. C22×D4 | C4×D79 | semidirect |
| 292. C2×C4⋊C4 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772650 | 2 |
| #23766231 | 2 |
| #23764237 | 2 |
| #23763343 | 2 |
| #23761307 | 2 |
| #23761286 | 2 |
| C79×#1507 | 2 |
| #9365 | 79 |